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Questions >> CBSE XII >> Math >> Matrices

Using properties of Determinants prove that : $\begin{vmatrix} a^2 & bc & ac+c^2 \\ a^2+ab & b^2 & ac \\ab & b^2+ac & c^2 \end{vmatrix}=4a^2b^2c^2$

asked Jan 24, 2013 by meena.p

0 answers

Prove that $\begin{vmatrix} x-3 & x-4 & x-a \\ x-2 & x-3 & x-b \\ x-1 & x-2 & x-c \end{vmatrix}=0,$ where a,b,c are in A.P

asked Jan 24, 2013 by meena.p

0 answers

Inverse of a square matrix is unique. Give an example to prove it?

asked Jan 24, 2013 by meena.p

0 answers

If $A=\begin{bmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}\;and\;A+A^T=1.$ Find the possible values of $\theta=\large\pi/3.$

asked Jan 24, 2013 by meena.p

0 answers

If $\begin{bmatrix} p & q \\ r & -p \end{bmatrix}$ is such that $A^2=1$ then find the value of $1-p^2+qr$

asked Jan 24, 2013 by meena.p

0 answers

If a+b+c=0 anb $\begin{vmatrix} a-x & a & b \\ c & b-x & a \\ b & a & c-x \end{vmatrix}$ then prove that either x=0 or $x= \pm\sqrt{\frac{3}{2}(a^2+b^2+c^2)}$

asked Jan 24, 2013 by meena.p

0 answers

Using elementary transformations, find the inverse of the following matrix : $\begin{bmatrix} 1 & 2 & 3 \\ 2 & 5 & 7 \\ -2 & -4 & -5 \end{bmatrix}$

asked Jan 2, 2013 by thanvigandhi_1

1 answer

True or False: $(AB)^{-1}=A^{-1}B^{-1},$ where A and B are invertible matrices satisfying commutative property with respect to multiplication.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: If A is skew symmetric matrix, then $A^2$ is a symmetric matrix.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: If $A =\begin{bmatrix} 2 & 3 & 1 \\ 1 &4 & 2 \end{bmatrix}\; and\; B=\begin{bmatrix}2 & 3 \\ 4& 5 \\ 2 & 1 \end{bmatrix},$ then AB and BA are defined and equal.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: AA' is always a symmetric matrix for any matrix A.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: If A,B and C are square matrices of same order, then AB = AC always implies that B=C.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: If (AB)' = B'A', where A and B are not square matrices, then number of rows in A is equal to number of columns in B and number of columns in A is equal to number of rows in B.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: If A and B are any two matrices of the same order, then (AB)' = A'B'.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: If each of the three matrices of the same order are symmetric matrix.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: If A and B are two square matrices of the same order , then AB = BA.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: Transpose of a column matrix is a column matrix.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: If a matrix AB = 0, then A=0 or B=0 or both A and B are null matrices.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: If A and B are two matrices of the same order, then A-B = B-A.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: If A and B are two square matrices of the same order , then A+B = B+A.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: A square matrix where every element is unity is called an identify matrix.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: Matrix multiplication is commutative.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: Matrix addition is associative as well as commutative.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: Matrices of different order can not be subtracted.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: Two matrices are equal if they have same number of rows and same number of columns.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: Matrices of any order can be added.

asked Dec 24, 2012 by sreemathi.v

1 answer

True or False: A matrix denotes a number.

asked Dec 24, 2012 by sreemathi.v

1 answer

In applying one or more row operations while finding $A^{-1}$ by elementary row operations, we obtain all zeros in one or more, then $A^{-1}$ ________ .

asked Dec 24, 2012 by sreemathi.v

1 answer

If A and B are symmetric matrices of same order, then AB is symmetric if and only if ___________ .

asked Dec 24, 2012 by sreemathi.v

1 answer

If A is symmetric matrix, then B'AB is ________ .

asked Dec 24, 2012 by sreemathi.v

1 answer

If A and B are symmetric matrices,then $\quad AB-BA\;is\;a\;\text{_______}$

asked Dec 24, 2012 by sreemathi.v

1 answer

If A is skew symmetric, then kA is a __________. (k is any scalar).

asked Dec 24, 2012 by sreemathi.v

1 answer

If A and B are square matrices of the same order,then $\quad (AB)'=\text{________}.$

asked Dec 24, 2012 by sreemathi.v

1 answer

If A is a skew symmetric matrix, then $A^2$ is a ____________ .

asked Dec 24, 2012 by sreemathi.v

1 answer

If A is a symmetric matrix, then $A^3$ is a _________ matrix.

asked Dec 24, 2012 by sreemathi.v

1 answer

Matrix multiplication is __________ over addition.

asked Dec 24, 2012 by sreemathi.v

1 answer

A matrix which is not a square matrix is called a __________ matrix.

asked Dec 24, 2012 by sreemathi.v

1 answer

The product of any matrix by the scalar ____________ is the null matrix.

asked Dec 24, 2012 by sreemathi.v

1 answer

The negative of a matrix is obtained by multiplying it by

asked Dec 24, 2012 by sreemathi.v

1 answer

Sum of two skew symmetric matrices is always ____________ matrix.

asked Dec 24, 2012 by sreemathi.v

1 answer

________________ matrix is both symmetric and skew symmetric matrix.

asked Dec 24, 2012 by sreemathi.v

1 answer

On using elementary row operations $R_2\times R_1-3R_2$ in the following matrix equation $\begin{bmatrix}4 & 2\\3 & 3\end{bmatrix}=\begin{bmatrix}1 & 2\\0 & 3\end{bmatrix}\begin{bmatrix}2 & 0\\1 & 1\end{bmatrix}$ ,we have:

asked Dec 24, 2012 by sreemathi.v

1 answer

On using elementary column operations $C_2\times C_2-2C_1$ in the following matrix equation $\begin{bmatrix}1 & 3\\2 & 4\end{bmatrix}=\begin{bmatrix}1 & 1\\0 & 1\end{bmatrix}\begin{bmatrix}3 & 1\\2 & 4\end{bmatrix}, \text{we have}$

asked Dec 24, 2012 by sreemathi.v

1 answer

For any two matrices A and B,we have

asked Dec 24, 2012 by sreemathi.v

1 answer

If A is a square matrix such that $A^2=I$ ,then $(A-I)^3+(A+I)^3-7A$ is equal to $(A)\quad A\quad (B)\quad I-A\quad (C)\quad I +A\quad(D)\quad 3A$

asked Dec 24, 2012 by sreemathi.v

1 answer

If A and B are matrices of same order ,then (AB'-BA') is a

asked Dec 24, 2012 by sreemathi.v

1 answer

If A is matrix of order $m\times n$ and B is a matrix such that AB' and B'A are both defined,then order of matrix B is

asked Dec 24, 2012 by sreemathi.v

1 answer

The matrix $\begin{bmatrix}0 & 5 & 8\\5 & 0 & 12\\8 & 12 & 0\end{bmatrix}$ is

asked Dec 24, 2012 by sreemathi.v

1 answer

The matrix $\begin{bmatrix}1 & 0 & 0\\0 & 2 & 0\\0 & 0 & 4\end{bmatrix}$ is a

asked Dec 23, 2012 by sreemathi.v

1 answer

If Matrix $A=[a_{ij}]_{2\times 3},$ where $a_{ij} \begin{array}{ 1 1}=1\;if\;i\neq j\\=0\;if\;i=j\end{array}$ then $\;A^2\;$ is equal to:

asked Dec 23, 2012 by sreemathi.v

1 answer

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